Sometimes students may encounter complex quadratics factorise involving \( x^2, y^2, xy, x \) and \( y \). Consider factorising by only either \( x \) or \( y \). The following examples take through factorising \( y \) first, then \( x\). Example 1 Factorise \( x^2 + 2xy + 5x + y^2+ 5y […]

# Tag Archives: Quadratic Factorise

# Fractions involving Quadratic Terms: Non-Monic Expressions

# Fractions involving Quadratic Terms: Common Factors

Transcript See! 2 is common and same here, 3 is common, so take out your common factors first.So take 2 out and here take 3 out and make sure you got the right remainders in the brackets, okay? So now that we’ve simplified that by taking our common factors. Now we can apply our quadratics. […]

# Fractions involving Quadratic Terms: Difference of Squares

Transcript You can see that we’ve got a quadratic on both numerator and denominator. So let’s go factorize those individually. I’m going to start with the numerator use your usual cross method x and x. I know that’s going to be negative and negative because that’s positive and that’s negative, so negative negative is what […]

# Fractions involving Quadratic Terms: Monic Expressions

Transcript The numerator, first of all, I’m going to use x and x because it’s negative. I know I’m going to use positive and a negative number. I’m going to start with a positive 4. So x times positive 4 is 4x. The other one will be negative 1. Now as I said guys some […]

# Fractions involving Quadratic and Linear Terms: Difference of Squares

Transcript It’s a square number minus the square number because you know that 16 is 4 squared, so it’s going to be, let’s get, as I said, 4 squared. So square minus square, how do we factorize that? Everyone should know it will be x plus 4, x minus 4, okay? Or the other way […]

# Fractions involving Quadratic and Linear Terms: Common Factors

Transcript All right! Again, we’ve got a fraction and you can see we have a quadratic on the numerator. So again our cross method. So my two x’s, it’s positive 20, so it’s positive, so it could be positive positive or negative negative but since this is negative we must have negative negative. So I’m […]

# Fractions involving Quadratic and Linear Terms: Monic Expressions

Transcript It says simplify that fraction there and you can see we have a quadratic on the numerator.Now before we get started guys, whenever we’re trying to simplify any type of algebraic fractions, always trying to factorize. So we just need to factorize the numerator and the denominator individually and then once we factorize it […]

# Factorising Difference of Squares: Higher Order Factorise

Transcript Okay! This time’s a little bit different because I’ve got power of 4. But that’s okay guys, I’m going to make it into that form, square minus the square, difference of two squares. See here guys, x4 and y4. I’m going to change that to x squared, squared. And this one is y squared, […]

# Factorising Difference of Squares: Polynomial Terms and Common Factors

Transcript Now! This one, we don’t really need to do much and this one, it’s so this one is x squared and this one is 2x minus 1 squared. They already did it for you. They already put it as two square numbers. It’s a square number minus a square number. So this is your […]